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Large Deviations Principle for Stochastic Delay Differential Equations with Super-linearly Growing Coefficients
We utilize the weak convergence method to establish the Freidlin–Wentzell large deviations principle (LDP) for stochastic delay differential...
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Functional Large Deviations for Kac–Stroock Approximation to a Class of Gaussian Processes with Application to Small Noise Diffusions
In this paper, we establish the functional large deviation principle (LDP) for the Kac–Stroock approximations of a wild class of Gaussian processes...
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Mittag–Leffler Euler Integrator and Large Deviations for Stochastic Space-Time Fractional Diffusion Equations
Stochastic space-time fractional diffusion equations often appear in the modeling of the heat propagation in non-homogeneous medium. In this paper,...
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Large Deviation Principle for a Class of Stochastic Partial Differential Equations with Fully Local Monotone Coefficients Perturbed By Lévy Noise
The asymptotic analysis of a class of stochastic partial differential equations (SPDEs) with fully local monotone coefficients covering a large...
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Rigorous Results in Space-Periodic Two-Dimensional Turbulence
We survey the recent advance in the rigorous qualitative theory of the 2d stochastic Navier–Stokes system that are relevant to the description of...
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LDP and CLT for SPDEs with transport noise
In this work we consider solutions to stochastic partial differential equations with transport noise, which are known to converge, in a suitable...
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Large Deviations and Averaging for Stochastic Tamed 3D Navier–Stokes Equations with Fast Oscillations
In this paper, we first study the strong averaging principle for stochastic tamed 3D Navier–Stokes equation with fast oscillations, which can be...
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Analysis of stochastic neutral fractional functional differential equations
This work deals with the large deviation principle which studies the decay of probabilities of certain kind of extremely rare events. We consider...
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Large deviation principle for stochastic convective Brinkman–Forchheimer equations perturbed by pure jump noise
This paper concerns some asymptotic analysis of stochastic convective Brinkman–Forchheimer (SCBF) equations subjected to multiplicative pure jump...
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Fluctuating-rate model with multiple gene states
Multiple phenotypic states of single cells often co-exist in the presence of positive feedbacks. Stochastic gene-state switchings and low copy...
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Large Deviation Principle for Multi-Scale Stochastic Systems with Monotone Coefficients
The Freidlin–Wentzell’s large deviation principle is established for a class of multi-scale stochastic models involving slow–fast components, where...
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Large deviation principle for quasi-stationary distributions and multiscale dynamics of absorbed singular diffusions
The present paper is devoted to the investigation of an important family of absorbed singular diffusion processes exhibiting long transient dynamics,...
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Uniform Large Deviation Principle for the Solutions of Two-Dimensional Stochastic Navier–Stokes Equations in Vorticity Form
The main objective of this paper is to demonstrate the uniform large deviation principle (UDLP) for the solutions of two-dimensional stochastic...
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Stochastic differential equations
We identify the solution to a rough differential equation driven by the Itˆo or Stratonovich lift of Brownian motion with the solution to the...
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Stochastic Doubly Nonlinear PDE: Large Deviation Principles and Existence of Invariant Measure
In this paper, we establish large deviation principle for the strong solution of a doubly nonlinear PDE driven by small multiplicative Brownian...
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Large Deviation Principle for McKean–Vlasov Quasilinear Stochastic Evolution Equations
This paper is devoted to investigating the Freidlin–Wentzell’s large deviation principle for a class of McKean–Vlasov quasilinear SPDEs perturbed by...
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Central limit type theorem and large deviation principle for multi-scale McKean–Vlasov SDEs
The main aim of this work is to study the asymptotic behavior for multi-scale McKean–Vlasov stochastic dynamical systems. Firstly, we obtain a...
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Large Deviations of Stochastic Heat Equations with Logarithmic Nonlinearity
In this paper, we establish a large deviation principle for the solutions to the stochastic heat equations with logarithmic nonlinearity driven by...